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Recurrence Relations : Stirling Numbers

A stirling number Snk is defined as the number of ways to partition the set of positive numbers (1,2,3....n) into k non empty subsets.

By considering whether or not the singleton subset (n) is included in a partition or not show: Snk = Sn-1,k-1 - kSn-1,k

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Recurrence Relations and Stirling Numbers are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.